Motivic p-adic tame cohomology
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866916811296997376 |
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| author | Merici, Alberto |
| author_facet | Merici, Alberto |
| contents | We construct a comparison functor between ($\mathbf{A}^1$-local) tame motives and ($\overline{\square}$-local) log-étale motives over a field $k$ of positive characteristic. This generalizes Binda--Park--Østvær's comparison for the Nisnevich topology. As a consequence, we construct an $E_\infty$-ring spectrum $H\mathbb{Z}/p^m$ representing mod $p^m$ tame motivic cohomology: the existence of this ring spectrum and the usual properties of motives imply some results on tame motivic cohomology, which were conjectured by Hübner--Schmidt. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_02499 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Motivic p-adic tame cohomology Merici, Alberto Algebraic Geometry K-Theory and Homology Number Theory 14F30 (Primary), 14F42, 19E15 We construct a comparison functor between ($\mathbf{A}^1$-local) tame motives and ($\overline{\square}$-local) log-étale motives over a field $k$ of positive characteristic. This generalizes Binda--Park--Østvær's comparison for the Nisnevich topology. As a consequence, we construct an $E_\infty$-ring spectrum $H\mathbb{Z}/p^m$ representing mod $p^m$ tame motivic cohomology: the existence of this ring spectrum and the usual properties of motives imply some results on tame motivic cohomology, which were conjectured by Hübner--Schmidt. |
| title | Motivic p-adic tame cohomology |
| topic | Algebraic Geometry K-Theory and Homology Number Theory 14F30 (Primary), 14F42, 19E15 |
| url | https://arxiv.org/abs/2408.02499 |